How can I automatically have an Object which is related to a Lead, create a lookup relationship with Account and Contact after Lead conversion?

So, I create a custom object called Form Submissions which currently has a lookup relationship with the Lead object. This relationship occurs automatically through the integration I created between Gravity Forms and Salesforce.

However, I'm struggling to figure out how to carry the relationship forward to Account and Contact objects when the Lead is converted. I'd like end-users to be able to see related Form Submissions when they view a Contact or an Account.

This is what the Form Submission object page looks like right now. I want those 2 lookup fields to populate automatically when the lead converts. I'm thinking maybe a Flow, but I'm not sure about the logic?

Any suggestions or best practices to achieve this?

Thanks in advance!

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